/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */
/* C4723: potential divide by zero. */
#pragma warning ( disable : 4723 )
#endif

/* __ieee754_log10(x)
 * Return the base 10 logarithm of x
 *
 * Method :
 *	Let log10_2hi = leading 40 bits of log10(2) and
 *	    log10_2lo = log10(2) - log10_2hi,
 *	    ivln10   = 1/log(10) rounded.
 *	Then
 *		n = ilogb(x),
 *		if(n<0)  n = n+1;
 *		x = scalbn(x,-n);
 *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
 *
 * Note 1:
 *	To guarantee log10(10**n)=n, where 10**n is normal, the rounding
 *	mode must set to Round-to-Nearest.
 * Note 2:
 *	[1/log(10)] rounded to 53 bits has error  .198   ulps;
 *	log10 is monotonic at all binary break points.
 *
 * Special cases:
 *	log10(x) is NaN with signal if x < 0;
 *	log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
 *	log10(NaN) is that NaN with no signal;
 *	log10(10**N) = N  for N=0,1,...,22.
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following constants.
 * The decimal values may be used, provided that the compiler will convert
 * from decimal to binary accurately enough to produce the hexadecimal values
 * shown.
 */

#include "math_libm.h"
#include "math_private.h"

static const double
two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */

static const double zero = 0.0;

double attribute_hidden __ieee754_log10(double x)
{
    double y, z;
    int32_t i, k, hx;
    u_int32_t lx;

    EXTRACT_WORDS(hx, lx, x);

    k = 0;
    if(hx < 0x00100000) {                   /* x < 2**-1022  */
        if(((hx & 0x7fffffff) | lx) == 0) {
            return -two54 / zero;  /* log(+-0)=-inf */
        }
        if(hx < 0) {
            return (x - x) / zero;  /* log(-#) = NaN */
        }
        k -= 54;
        x *= two54; /* subnormal number, scale up x */
        GET_HIGH_WORD(hx, x);
    }
    if(hx >= 0x7ff00000) {
        return x + x;
    }
    k += (hx >> 20) - 1023;
    i  = ((u_int32_t)k & 0x80000000) >> 31;
    hx = (hx & 0x000fffff) | ((0x3ff - i) << 20);
    y  = (double)(k + i);
    SET_HIGH_WORD(x, hx);
    z  = y * log10_2lo + ivln10 * __ieee754_log(x);
    return  z + y * log10_2hi;
}

/*
 * wrapper log10(X)
 */
#ifndef _IEEE_LIBM
double log10(double x)
{
    double z = __ieee754_log10(x);
    if(_LIB_VERSION == _IEEE_ || isnan(x)) {
        return z;
    }
    if(x <= 0.0) {
        if(x == 0.0) {
            return __kernel_standard(x, x, 18);  /* log10(0) */
        }
        return __kernel_standard(x, x, 19); /* log10(x<0) */
    }
    return z;
}
#else
strong_alias(__ieee754_log10, log10)
#endif
libm_hidden_def(log10)
